Enhancement of download multi-user multiple-input multiple-output wireless communications

ABSTRACT

A method implemented in a user equipment configured to be used in a multi-user (MU) multiple-input multiple-output (MIMO) wireless communications system is disclosed. The method includes transmitting to a base station a first channel state information (CSI) report determined according to a single-user (SU) MIMO rule, and transmitting to the base station a second CSI report determined according to an MU-MIMO rule. Other methods, apparatuses, and systems also are disclosed.

This application is a divisional of co-pending U.S. patent applicationSer. No. 13/456,881, entitled, “ENHANCEMENT OF DOWNLOAD MULTI-USERMULTIPLE-INPUT MULTIPLE-OUTPUT WIRELESS COMMUNICATIONS,” filed on Apr.26, 2012, which in turn claims the benefit of U.S. ProvisionalApplication No. 61/480,690, entitled, “Enhancements to DL MU-MIMO,”filed Apr. 29, 2011, U.S. Provisional Application No. 61/543,591,entitled, “Enhancements to DL MU-MIMO,” filed Oct. 5, 2011, and U.S.Provisional Application No. 61/556,560, entitled, “DL MU-MIMOEnhancement via Residual Error Norm Feedback,” filed Nov. 7, 2011, ofwhich the contents of all are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to wireless communications system and moreparticularly to multi-user (MU) multiple-input multiple-output (MIMO)wireless communications system.

The present invention considers the problem of designing efficientchannel state information (CSI) feedback schemes in order to allowimproved multi-user multi-input multi-output resource allocation at abase-station (BS), resulting in increased system spectral efficiency. Acell in which multiple users feedback CSI and the BS performs MU-MIMOresource allocation is depicted in FIG. 1.

Referring to FIG. 1, user terminals 110, e.g. users 1 (111) to K (119),send quantized channel feedbacks 120 to base station 130. At basestation 130, DL (downlink) MU-MIMO resource allocation 140 is performedaccording to quantized channel feedbacks 120 and streams, e.g. user 1stream 151 to user K stream 159, are subjected to RB (resource block)and/or MCS (modulation and coding scheme) allocation and transmitprecoding 160. Signals are transmitted via n_(T) antennas from basestation 130 and received by n_(R) antennas, for example, at user 1(111).

Note that the quality of resource allocation done by the BS depends onthe accuracy of each user's CSI report. On the other hand, allowing avery accurate CSI feedback can result in a large signaling overhead. Thekey challenges that need to be overcome before spectral efficiency gainsfrom MU-MIMO can realized are, for example, as follows:

-   -   Improving CSI accuracy without a large signaling overhead, or    -   Exploiting the enhanced CSI reports at the BS in an efficient        manner.

In order to solve the above problem, others have proposed varioussolutions, such as increasing CSI feedback overhead; CSI feedback underassumptions on BS scheduling; and complex algorithms for jointscheduling.

CQI (Channel Quality Indicator) PMI (Precoding Matrix Indicator)reporting enhancements targeting DL MU-MIMO operations on PUSCH 3-1 aswell as PUSCH 3-2 were considered by several companies [1]. The proposedenhancement to PUSCH 3-2 comprised enabling sub-band PMI reporting inaddition to the sub-band CQI reporting. On the other hand, enhancementsto PUSCH 3-1 that were considered suggested that in addition to 3rdGeneration Partnership Project (3GPP) Release (Rel-) 8 Mode 3-1feedback, a user equipment (UE) can be configured via higher layersignalling to report as follows:

-   -   A wideband PMI calculated assuming restricted rank equal to one,        along with a per subband CQI targeting MU-MIMO operation.    -   The MU-MIMO CQI is computed assuming the interfering PMIs are        orthogonal to the single-user (SU) MIMO rank 1 PMI and for 4 TX,        the total number of co-scheduled layers is assumed to be 4 at        the time of MU CQI computation [1].

We propose a broad framework for enhanced CSI reporting by the users inorder to obtain an improvement in MU-MIMO performance. We alsoillustrate mechanisms using which the eNodeB (eNB) can exploit suchenhanced CSI feedback. System level simulations show that a simple formof enhanced feedback results in substantial system throughputimprovements in homogenous networks and more modest improvements overheterogeneous networks.

[1] Alcatel-Lucent, Alcatel-Lucent Shanghai Bell, AT&T, ETRI, IceraInc., LG Electronics, Marvell, NEC, New Postcom, Pantech, Qualcomm, RIM,Samsung, Texas Instruments, “Way Forward on CQI/PMI reportingenhancement on PUSCH 3-1 for 2, 4 and 8 TX,” 3GPP TSG RAN WG1 R1-10580162bis, Xian, China, October 2010.

BRIEF SUMMARY OF THE INVENTION

An objective of the present invention is to achieve a high spectralefficiency, for example, even around a cell edge in an MU-MIMO wirelesscommunications system.

An aspect of the present invention includes a method implemented in auser equipment configured to be used in a multi-user (MU) multiple-inputmultiple-output (MIMO) wireless communications system, comprising:transmitting to a base station a first channel state information (CSI)report determined according to a single-user (SU) MIMO rule; andtransmitting to the base station a second CSI report determinedaccording to an MU-MIMO rule.

Another aspect of the present invention includes a method implemented ina base station configured to be used in a multi-user (MU) multiple-inputmultiple-output (MIMO) wireless communications system, comprising:receiving from a user equipment a first channel state information (CSI)report determined according to a single-user (SU) MIMO rule; andreceiving from the user equipment a second CSI report determinedaccording to an MU-MIMO rule.

Still another aspect of the present invention includes a multi-user (MU)multiple-input multiple-output (MIMO) wireless communications system,comprising: a base station; and a user equipment, wherein the userequipment transmits to the base station a first channel stateinformation (CSI) report determined according to a single-user (SU) MIMOrule, and a second CSI report determined according to an MU-MIMO rule.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an illustrative diagram for CSI feedback.

FIG. 2 depicts an illustrative diagram for multiplexing SU-CSI andenhanced feedback.

FIG. 3 depicts an illustrative diagram for combining SU-CSI and enhancedfeedback.

FIG. 4 depicts an illustrative diagram for multiplexing SU-CSI andcombined CSI feedback.

DETAILED DESCRIPTION

We consider a downlink comprising K users and multiple orthogonal RBsthat are available in each scheduling interval. We first model theactual received signal vector that the user will see on a representativeresource element in an RB, if it is scheduled on that RB, asy ₁ =H ₁ *U ₁ s ₁ +H ₁ *U ₁ s ₁ +η₁  (1)where y₁ represents the N×1 received signal vector on an RB (N being thenumber of receive antennas) and H₁ represents the M×N channel matrix (Mbeing the number of transmit antennas) with H₁* denoting its Hermitian.U₁ and U ₁ represent the transmit precoding matrices used by the BS totransmit data to user-1 and the other co-scheduled users (or userequipments), respectively, and s₁ and s ₁ represent the transmit symbolvectors intended for user-1 and the other co-scheduled users,respectively. Finally η₁, represents the additive noise vector. Notethat under MU-MIMO transmission on that RB U ₁ will be a non-zero matrixwhereas under SU-MIMO transmission on that RB U ₁ will be a zero matrix.

The model in equation (1) is the model in the aftermath of scheduling.The scheduling which involves RB, MCS and transmit precoder allocationby the BS is done by the BS scheduler whose input is the quantized CSI(referred to henceforth as just CSI) fed back by the users.

The conventional procedure employed by the users to report CSI is tocompute a rank indicator (RI), precoding matrix indicator (PMI), whichtogether determine a precoder from a quantization codebook, along withup-to 2 channel quality indicators or indices (CQI(s)). Note that thecolumns of the selected precoder represent a set of preferred channeldirections and the CQI(s) represent quantized SINRs (signal tointerference plus noise ratios). Further, for a rank R precoder, R SINRs(one for each column) can be recovered from the up-to 2 CQI(s). Moreimportantly, this CSI is computed by the user using SU-MIMO rules, i.e.,after assuming that it alone will be scheduled on an RB. Such CSI isreferred to here as SU-CSI.

Clearly, if the BS wants to do MU-MIMO transmissions on an RB then itmay, modify the SU-CSI reported by the users in order to do proper MCSassignment and RB allocation. However, even after such modificationsMU-MIMO performance is degraded due to a large mismatch between UEreported SU-CSI and the actual channel conditions that UE will see on anRB with MU-MIMO transmissions.

In order to address this problem we propose enhanced CSI feedback alongwith a finer model that can exploit the enhanced CSI feedback report andcan be used for better MU-MIMO resource allocation at the BS. The finermodel, a post scheduling model, can be given by, but not restricted to,y ₁ ={circumflex over (D)} ₁ ^(1/2) {circumflex over (V)} ₁ ^(†) U ₁ s ₁+{circumflex over (D)} ₁ ^(1/2)({circumflex over (V)} ₁ ^(†) +R ₁ ^(†) Q₁ ^(†))U ₁ s ₁ +η₁  (2)where {circumflex over (D)}₁ ^(1/2) is a diagonal matrix of effectivechannel gains, {circumflex over (V)}₁ denotes a semi-unitary matrixwhose columns represent preferred channel directions, Q₁ is asemi-unitary matrix whose columns lie in the orthogonal complement of{circumflex over (V)}₁, i.e. Q₁ ^(†){circumflex over (V)}₁=0, and R₁ isa matrix which satisfies the Frobenius-norm constraint ∥R₁∥_(F) ²≦ε₁ ²for some ε₁>0.

-   -   MU-CQI reporting: The UE is configured to also report additional        CQI computed using MU-MIMO rules and possibly an additional PMI.        To compute MU-CQI corresponding to a precoder Ĝ₁, the UE assumes        a post-scheduling model as in equation (2) in which {circumflex        over (D)}₁ ^(1/2), {circumflex over (V)}₁ are equal to the        diagonal matrix of the dominant unquantized singular values and        the dominant unquantized right singular vectors, respectively,        of its downlink channel matrix. It sets U₁=Ĝ₁ and assumes that        the columns of U ₁ are isotropically distributed in the subspace        defined by I−Ĝ₁Ĝ₁ ^(†) (orthogonal complement of Ĝ₁). In        addition it assumes Q₁=0 which is reasonable in this case since        {circumflex over (V)}¹ is taken to contain all the unquantized        dominant singular vectors so no significant interference can be        received from signals in its orthogonal complement. Then, to        compute MU-SINRs the UE can be configured to assume a particular        number of columns in U ₁ and either an equal power per scheduled        stream or a non-uniform power allocation in which a certain        fraction of energy per resource element energy per resource        element (EPRE) is shared equally among columns of U ₁ with        another fraction (possibly the remaining fraction) being shared        equally among columns in U ₁ .    -   Enhanced CSI Reporting (SU-MIMO CSI and Residual Error): The UE        can be configured for enhanced CSI reporting. Suppose that using        SU-MIMO rules the UE determined a precoder Ĝ₁ of a preferred        rank r₁ and the corresponding quantized SINRs {SI{circumflex        over (N)}R₁ ^(i)}_(i=1) ^(r) ¹ . In order to determine the        residual error, the UE assumes a post-scheduling model as in        equation (2) in which

${\hat{D}}_{1} = {\frac{r_{1}}{\rho_{1}}{diag}\left\{ {{{SI}\hat{N}R_{1}^{1}},\ldots\mspace{14mu},{{SI}\hat{N}R_{1}^{r_{1}}}} \right\}}$and {circumflex over (V)}₁=Ĝ₁. Then let

P₁^(⊥) = I − Ĝ₁Ĝ₁^(†)denote the projection matrix whose range is the orthogonal complement ofĜ₁. Let us refer to the matrix

$E_{1}\overset{\Delta}{=}{Q_{1}R_{1}}$as the (normalized) residual error matrix and the matrix C₁=E₁ ^(†)E₁ asthe residual error correlation matrix and note that C₁=D₁ ^(−1/2)F₁H₁^(†)P₁ ^(⊥)H₁F₁ ^(†)D₁ ^(−1/2). The UE can be configured to report someapproximation of either the residual error matrix or the residual errorcorrelation matrix. These include:

-   -   Quantizing and reporting the dominant diagonal values of R1        along with the corresponding columns in Q₁.    -   Quantizing and reporting the diagonal values of C₁    -   Quantizing and reporting the trace of

$C_{1},{\varepsilon_{1}^{2} = {{{tr}\left( C_{1} \right)} = {{tr}\left( {F_{1}H_{1}^{\dagger}P_{1}^{\bot}H_{1}F_{1}^{\dagger}{\overset{\sim}{D}}_{1}^{- 1}} \right)}}}$which can be thought of as the normalized total residual error.

The BS can configure the user to report a particular enhanced feedbackform. A simple example of the enhanced feedback form is the residualerror norm,ε₁=√{square root over (tr(F ₁ H ₁ ^(†) P ₁ H ₁ F ₁ ^(†) {tilde over (D)}₁ ⁻¹))}   (3)where tr(.) denotes the trace operation, F₁H₁ ^(†) denotes the filtereduser channel, and P₁=(I−{circumflex over (V)}₁{circumflex over (V)}₁^(†)) is a projection matrix. PMI V₁ of some rank r₁ and r₁ quantizedSINRs {SI{circumflex over (N)}R₁ ^(i)}_(i=1) ^(r) ¹ are determined usingSU-MIMO rules {tilde over (D)}=diag {SI{circumflex over (N)}R₁ ¹, . . ., SI{circumflex over (N)}R₁ ^(r) ¹ }. Various other forms for theenhanced feedback and various other norms for the residual error canapply to the enhanced feedback.

We list several flow diagrams that describe aspects of the invention. Ineach figure, the flow diagram describes the operations that areconducted at a user-terminal. The operations are enabled by signalingfrom the eNB (or base-station) certain parameters on a downlink(feed-forward) control channel that are then received as inputs by theuser. The feed-back is sent by the user on an uplink (feed-back) controlchannel and is received by the eNB. The parameters signaled by thebase-station to a user may be interpreted by that user in a particularway that is described in detail in the further system details. Moreover,wherever applicable, the feedback sent by the user may allow the eNB tounambiguously determine the portion of the feedback determined by theuser as SU-CSI and the portion determined as per the enhanced feedbackform.

In each channel state information (CSI) reporting interval the userreports its CSI. The BS (or eNB) can configure a user for periodic CSIreporting and fix the periodicity and offset which together determinethe exact sequence of intervals for which the user may report its CSI.This sequence will be henceforth referred to as the sequence for CSIreporting.

The user equipment can transmit to the base station an SU-CSI feedbackand an enhanced CSI feedback, which are received by the base station.The transmission and the reception can be performed in a various ways asfollows:

1. Multiplexing SU-CSI and Enhanced Feedback

In order to obtain the benefits of accurate MU-MIMO resource allocationwithout excessive feedback overhead, the eNB can multiplex intervals inwhich the user reports enhanced feedback with the ones in which itreports its SU-CSI feedback without enhanced feedback. The periodicityand offset of the sub-sequence formed by intervals designated forenhanced feedback within the sequence for CSI reporting can beconfigured by the eNB, based on factors such as user mobility.

As shown in FIG. 2, at step 201, a UE receives residual error formconfiguration from a BS and receives also sequence and sub-sequenceconfiguration information. Next, at step 202, the UE determines SU-CSIin each interval configured for SU-CSI report or determines enhanced CSIin each interval configured for enhanced CSI report. Then, at step 203,the UE feeds back the CSI to the BS.

Several ways of further reducing enhanced CSI feedback are described inthe further system details. These include, for instance, letting theprecoder used for computing the enhanced CSI be a function of previouslyreported precoder(s) contained in SU-CSI reports and/or reporting one ormore components in the enhanced CSI feedback in a wideband fashionand/or reporting one or more components in the enhanced CSI feedback ina differential fashion.

2. Combining SU-CSI and Enhanced Feedback

In the second class of feedback schemes, the user combines SU-MIMO CSIreport and enhanced CSI report and feeds them back in each interval.

As shown in FIG. 3, at step 301, a UE receives residual error formconfiguration from a BS and receives also sequence and sub-sequenceconfiguration information. Next, at step 302, the UE determines in eachinterval configured for CSI report SU-CSI and enhanced CSI. Then, atstep 303, the UE feeds back combined CSI to the BS.

Methods of further reducing enhanced CSI feedback overhead are describedin the further system details. These include, for instance, letting theprecoder used for computing the enhanced CSI be a function of theprecoder computed for SU-CSI report and/or reporting one or morecomponents in the enhanced CSI feedback in a wideband fashion and/orreporting one or more components in the enhanced CSI feedback in adifferential fashion.

3. Multiplexing SU-CSI and Combined CSI Feedback

FIG. 4 shows another method of CSI reporting. At step 401, a UE receivesresidual error form configuration from a BS and receives also sequenceand sub-sequence configuration information. Next, at step 402, the UEdetermines SU-CSI in each interval configured for SU-CSI report ordetermines combined CSI for combined CSI reporting. Then, at step 403,the UE feeds back CSI to the BS.

In FIGS. 2, 3, and 4, the sequence information includes, for example,periodicity and offset for the SU CSI reporting and the sub-sequenceconfiguration information includes, for example, periodicity and offsetfor the enhanced CSI reporting. For example, the enhanced CSI reportincludes any indication, such as a quantized value, of the residualerror matrix or the residual error correlation matrix.

FIGS. 2, 3, and 4 may apply to MU-CQI reporting as well.

In conclusion, we considered enhancements to the MU-MIMO operation byenhancing the user CSI reporting which enables more accurate MU-MIMOSINR computation at the eNB and by a finer modeling of the receivedoutput seen by a user in the aftermath of scheduling. Our results usinga simple form of enhanced feedback show substantial system throughputimprovements in homogenous networks and improvements also inheterogeneous networks. One important feature of the gains obtained isthat they are quite robust in the sense that they are not dependent onan effective outer loop link adaptation (OLLA) implementation.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention.

The invention claimed is:
 1. A method implemented in a user equipmentconfigured to be used in a multi-user (MU) multiple-inputmultiple-output (MIMO) wireless communications system, the methodcomprising: transmitting to a base station a first channel stateinformation (CSI) report determined according to a single-user (SU) MIMOrule; transmitting to the base station a second CSI report determinedaccording to an MU-MIMO rule; and assuming a post scheduling model,wherein the post scheduling model can be expressed asy ₁ ={circumflex over (D)} ₁ ^(1/2) {circumflex over (V)} ₁ +U ₁ s ₁+{circumflex over (D)} ₁ ^(1/2)({circumflex over (V)} ₁ ⁺ +R ₁ ⁺ Q ₁ ⁺)U₁ s ₁ +η₁ where y₁ represents an N×1 received signal vector on arepresentative resource element in a resource block (RB), N being thenumber of receive antennas at the user equipment, {circumflex over (D)}₁^(1/2) is a diagonal matrix of effective channel gains, {circumflex over(V)}₁ denotes a semi-unitary matrix whose columns represent preferredchannel directions and {circumflex over (V)}₁ ⁺ represents Hermitian of{circumflex over (V)}₁, U₁ and U ₁ represent preceding matrices used bythe base station to transmit data to the user equipment and aco-scheduled user equipment, respectively, s₁ and s ₁ represent transmitsymbol vectors intended for the user equipment and the co-scheduled userequipment, respectively, Q₁ is a semi-unitary matrix whose columns liein the orthogonal complement of {circumflex over (V)}₁, and R₁ is amatrix which satisfies the Frobenius-norm constraint ∥R₁∥_(F) ²<ε₁ ², ε₁being the residual error norm, and η₁ represents an additive noisevector.
 2. The method of claim 1, wherein the first CSI report istransmitted in a first interval configured for SU CSI reporting and thesecond CSI report is transmitted in a second interval configured for thesecond CSI report.
 3. The method of claim 1, wherein the first CSIreport and the second CSI report are transmitted in a common intervalconfigured for CSI reporting.
 4. The method of claim 1, wherein thefirst CSI report is transmitted in a first interval configured for SUCSI reporting and the first CSI report and the second CSI report aretransmitted in a second interval configured for combined CSI reporting.5. The method of claim 1, further comprising: receiving at least one ofsequence configuration information and sub-sequence configurationinformation from the base station, wherein the sequence configurationinformation comprises at least one of first periodicity and first offsetfor the first CSI report, and wherein the sub-sequence configurationinformation comprises at least one of second periodicity and secondoffset for the second CSI report.
 6. The method of claim 1, wherein thefirst CSI report includes at least one of a preferred rank, a precoderof the preferred rank, and a corresponding quantized SINR (signal tointerference plus noise ratio).
 7. The method of claim 1, wherein thesecond CSI report comprises at least one of channel quality indicator(CQI) and a preceding matrix indicator (PMI).
 8. The method of claim 1,further comprising: assuming a particular number of columns in U ₁ ; andassuming either a substantially equal power per scheduled stream or anon-uniform power allocation in which a first fraction of energy perresource element (EPRE) is shared substantially equally among one ormore columns of U ₁ with a second fraction of the EPRE being sharedsubstantially equally among one or more columns in U ₁ , where U₁ and U₁ represent preceding matrices used by the base station to transmit datato the user equipment and a co-scheduled user equipment, respectively.9. The method of claim 8, further comprising: receiving from the basestation an indication of at least one of the first fraction of the EPREand the second fraction of EPRE.
 10. The method of claim 1, wherein Q₁⁺{circumflex over (V)}₁=0.
 11. The method of claim 1, wherein{circumflex over (D)}₁ ^(1/2) and {circumflex over (V)}₁ are equal todiagonal matrices of dominant unquantized singular values and dominantunquantized right singular vectors, respectively, of a downlink channelmatrix.
 12. The method of claim 1, further comprising: setting U1=Ĝ₁where Ĝ₁ is a precoder; and assuming the columns of U ₁ areisotropically distributed in the subspace defined by I−Ĝ₁Ĝ₁ ⁺(orthogonal complement Ĝ₁.
 13. The method of claim 1, furthercomprising: assuming Q₁=0.
 14. A method implemented in a base stationconfigured to be used in a multi-user (MU) multiple-inputmultiple-output (MIMO) wireless communications system, the methodcomprising: receiving from a user equipment a first channel stateinformation (CSI) report determined according to a single-user (SU) MIMOrule; receiving from the user equipment a second CSI report determinedaccording to an MU-MIMO rule and assuming a post scheduling model,wherein the post scheduling model can be expressed asy ₁ ={circumflex over (D)} ₁ ^(1/2) {circumflex over (V)} ₁ ⁺ U ₁ s ₁+{circumflex over (D)} ₁ ^(1/2)({circumflex over (V)} ₁ ⁺ +R ₁ ⁺ Q ₁ ⁺)U₁ s ₁ +η₁ where y₁ represents an N×1 received signal vector on arepresentative resource element in a resource block (RB), N being thenumber of receive antennas at the user equipment, {circumflex over (D)}₁^(1/2) is a diagonal matrix of effective channel gains, {circumflex over(V)}₁ denotes a semi-unitary matrix whose columns represent preferredchannel directions and {circumflex over (V)}₁ ⁺ represents Hermitian of{circumflex over (V)}₁, U₁ and U ₁ represent preceding matrices used bythe base station to transmit data to the user equipment and aco-scheduled user equipment, respectively, s₁ and s ₁ represent transmitsymbol vectors intended for the user equipment and the co-scheduled userequipment, respectively, Q₁ is a semi-unitary matrix whose columns liein the orthogonal complement of {circumflex over (V)}₁, and R₁ is amatrix which satisfies the Frobenius-norm constraint ∥R₁∥_(F) ²<ε₁ ², ε₁being the residual error norm, and η₁ represents an additive noisevector.
 15. A multi-user (MU) multiple-input multiple-output (MIMO)wireless communications system comprising: a base station; and a userequipment, wherein the user equipment transmits to the base station afirst channel state information (CSI) report determined according to asingle-user (SU) MIMO rule, and a second CSI report determined accordingto an MU-MIMO rule, wherein the user equipment assumes a post schedulingmodel, and wherein the post scheduling model can be expressed asy ₁ ={circumflex over (D)} ₁ ^(1/2) {circumflex over (V)} ₁ ⁺ U ₁ s ₁+{circumflex over (D)} ₁ ^(1/2)({circumflex over (V)} ₁ ⁺ +R ₁ ⁺ Q ₁ ⁺)U₁ s ₁ +η₁ where y₁ represents an N×1 received signal vector on arepresentative resource element in a resource block (RB), N being thenumber of receive antennas at the user equipment, {circumflex over (D)}₁^(1/2) is a diagonal matrix of effective channel gains, {circumflex over(V)}₁ denotes a semi-unitary matrix whose columns represent preferredchannel directions and {circumflex over (V)}₁ ⁺ represents Hermitian of{circumflex over (V)}₁, U₁ and U ₁ represent preceding matrices used bythe base station to transmit data to the user equipment and aco-scheduled user equipment, respectively, s₁ and s ₁ represent transmitsymbol vectors intended for the user equipment and the co-scheduled userequipment, respectively, Q₁ is a semi-unitary matrix whose columns liein the orthogonal complement of {circumflex over (V)}₁, and R₁ is amatrix which satisfies the Frobenius-norm constraint ∥R₁∥_(F) ²<ε₁ ², ε₁being the residual error norm, and η₁ represents an additive noisevector.